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A309603 Digits of the 10-adic integer (-11/9)^(1/3).

%I A309603 #22 Aug 12 2019 02:40:31
%S A309603 1,4,1,3,3,4,9,2,3,9,4,8,9,1,0,5,1,4,1,4,3,7,7,4,7,8,1,2,3,0,0,1,7,6,
%T A309603 1,8,9,4,1,4,2,9,9,0,3,2,5,7,9,3,3,2,2,8,7,5,8,2,0,8,7,4,5,1,2,2,6,5,
%U A309603 5,0,8,2,3,0,3,2,9,2,5,8,6,6,3,0,2,5,3,0,1,1,4,0,9,9,8,4,5,9,4,5
%N A309603 Digits of the 10-adic integer (-11/9)^(1/3).
%H A309603 Seiichi Manyama, <a href="/A309603/b309603.txt">Table of n, a(n) for n = 0..10000</a>
%F A309603 Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 1, b(n) = b(n-1) + 7 * (9 * b(n-1)^3 + 11) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.
%e A309603        1^3 == 1      (mod 10).
%e A309603       41^3 == 21     (mod 10^2).
%e A309603      141^3 == 221    (mod 10^3).
%e A309603     3141^3 == 2221   (mod 10^4).
%e A309603    33141^3 == 22221  (mod 10^5).
%e A309603   433141^3 == 222221 (mod 10^6).
%o A309603 (PARI) N=100; Vecrev(digits(lift(chinese(Mod((-11/9+O(2^N))^(1/3), 2^N), Mod((-11/9+O(5^N))^(1/3), 5^N)))), N)
%o A309603 (Ruby)
%o A309603 def A309603(n)
%o A309603   ary = [1]
%o A309603   a = 1
%o A309603   n.times{|i|
%o A309603     b = (a + 7 * (9 * a ** 3 + 11)) % (10 ** (i + 2))
%o A309603     ary << (b - a) / (10 ** (i + 1))
%o A309603     a = b
%o A309603   }
%o A309603   ary
%o A309603 end
%o A309603 p A309603(100)
%Y A309603 Cf. A165402, A309600, A309645.
%K A309603 nonn
%O A309603 0,2
%A A309603 _Seiichi Manyama_, Aug 09 2019